Quantitative analysis of the effect of end‐tidal carbon dioxide on regional cerebral oxygen saturation in patients undergoing carotid endarterectomy under general anaesthesia

Abstract

Aims

Regional cerebral oxygen saturation (rSO₂) is currently the most used measure in clinical practice to monitor cerebral ischaemia in patients undergoing carotid endarterectomy (CEA). Although end‐tidal carbon dioxide (P_ETCO₂) is known as a factor that influences rSO₂, the relationship between P_ETCO₂ and rSO₂ has not been quantitatively evaluated in patients with severe arteriosclerosis. This study aimed to evaluate the effect of P_ETCO₂ on rSO₂ in patients undergoing CEA under general anaesthesia.

Methods

The intervention to change P_ETCO₂ was conducted between skin incision and clamping of the carotid artery. The rSO₂ values were observed by changing P_ETCO₂ in the range of 25–45 mmHg. The P_ETCO₂–rSO₂ relationship was characterized by population analysis using a turnover model.

Results

In total, 1651 rSO₂ data points from 30 patients were used to determine the pharmacodynamic characteristics. Hypertension (HTN) and systolic blood pressure (SBP) were significant covariates on the slope factor in the stimulatory effect of P_ETCO₂ on rSO₂ and fractional turnover rate constant (k_out), respectively. The estimates of the parameters were k_out(min⁻¹): 3.59 for SBP <90 mmHg and 0.491 for SBP ≥90 mmHg, slope: 0.00321 for patients with HTN and 0.00664 for patients without HTN.

Conclusion

The presence of HTNattenuates the response of rSO₂ after a change in P_ETCO₂. When cerebral blood flow is in a state of decline caused by a decrease in SBP to <90 mmHg, the response of rSO₂ to P_ETCO₂ is increased. It is advisable to maintain SBP >90 mmHg in patients with HTNduring CEA.

What is Already Known about this Subject

• Regional cerebral oxygen saturation (rSO₂) increases with an increase in end‐tidal carbon dioxide (P_ETCO₂).

• A turnover model can be an appropriate method to describe a time delay between drug concentration and an endogenous effect.

What this Study Adds

• The response of rSO₂ to P_ETCO₂ increase was slower in patients with hypertension than in those without hypertension.

• When cerebral blood flow is in a state of decline caused by a decrease in systolic blood pressure to <90 mmHg, the response of rSO₂ to P_ETCO₂ is increased.

Introduction

Carotid endarterectomy (CEA) is a surgical procedure used to prevent stroke in patients with severe carotid stenosis caused by an atherosclerotic plaque 1. Cross‐clamping of the carotid artery is required to remove plaque at the bifurcation of the common carotid, which can lead to neurological derangement induced by impaired cerebral blood flow 2. Among the various neurological monitoring modalities, near‐infrared spectroscopy‐based regional cerebral oxygen saturation (rSO₂) is mainly used to monitor cerebral ischaemia in clinical practice 3, 4. In an earlier study, an 11.7% decrease in rSO₂ from the baseline value was set as the cut‐off value of neurological derangement under general anaesthesia 5. Although end‐tidal carbon dioxide (P_ETCO₂) is known as a factor that influences rSO₂ 6, the relationship between P_ETCO₂ and rSO₂ has not been quantitatively evaluated in patients with severe arteriosclerosis.

In a previous study, a time delay was observed between P_ETCO₂ and rSO₂ 7. The turnover model could appropriately describe it between drug concentration and effect 8. Moreover, the model is best conceptualized when the effect is an endogenous biomarker 8. Considering rSO₂ as an endogenous substance in the human body, the turnover model can be used to characterize the effect of P_ETCO₂ on rSO₂ 7.

The aim of this study was to quantitatively evaluate the dose–response relationship between P_ETCO₂ and rSO₂using a turnover model in patients undergoing CEA under general anaesthesia.

Materials and methods

Patient population

This clinical trial was approved by the Institutional Review Board of Asan Medical Center and was registered on an international clinical trials registry platform (http://cris.nih.go.kr; KCT0000179). Written informed consent was obtained from all patients. In total, 32 patients undergoing CEA under general anaesthesia were enrolled in this study. The indication for surgery was 70% stenosis of the internal carotid artery for symptomatic patients. Patients were excluded if they had a history of obstructive lung diseases, including asthma and chronic obstructive pulmonary disease. Two‐dimensional echocardiography and pulmonary function test were performed before surgery to evaluate the patient's physical condition.

Study procedure

All patients fasted for 6–8 h prior to surgery. For continuous blood pressure monitoring, a 20‐gauge catheter was inserted into a radial artery. Electrocardiography, pulse oximetry, P_ETCO₂ and invasive blood pressure (Datex‐Ohmeda S/5, Planar Systems, Inc., Beaverton, OR, USA) were monitored continuously. Throughout the surgery, these data were downloaded to personal computers using RS232C cables. The rSO₂ (INVOS 5100B, Covidien, Boulder, CO, USA) was monitored continuously and downloaded to a personal computer until recovery from anaesthesia. Sensors for rSO₂ were placed on the right and left forehead. The rSO₂ values from the right and left were averaged to evaluate the effect of P_ETCO₂ on rSO_2.The target concentrations of propofol and remifentanil were adjusted to maintain bispectral index (Covidien) values of <60 and stable haemodynamics. Systolic blood pressure (SBP) was maintained within the range of the resting values in the general ward, and were specific to each patient. If necessary, vasopressors and antihypertensive drugs were used to titrate the SBP during surgery. Tracheal intubation was performed after administering cisatracurium (0.2 mg kg⁻¹). The lungs of the patients were then ventilated with oxygen in air [1:2, fraction of inspired oxygen (FiO₂) = 0.47], and the tidal volume and ventilation rate were adjusted to maintain the P_ETCO₂ between 25 and 45 mmHg. Neuromuscular blockade was reversed by administering pyridostigmine and glycopyrrolate at the end of surgery.

Method of intervention to change P_ETCO₂

The intervention was conducted between skin incision and clamping of the carotid artery. Approximately 5 min after the start of skin incision, the tidal volume and ventilation rate were adjusted so that P_ETCO₂ was maintained at 25 mmHg. When P_ETCO₂ was maintained at 25 mmHg for more than 3 min, the tidal volume was halved and the ventilation rate was reduced to 2/3, which was maintained until P_ETCO₂ reached 45 mmHg. When P_ETCO₂ reached 45 mmHg, they were restored to the control values until P_ETCO₂ reached 25 mmHg. The time at which the tidal volume and ventilation rate were decreased to raise P_ETCO₂ to 45 mmHg was defined as the reference time. The intervention period was set as the time elapsed between the reference time and the time when P_ETCO₂ reached 25 mmHg. The intervention period lasted 27.1 ±5.8 min. After the intervention period, P_ETCO₂ was maintained between 35 and 45 mmHg until the end of the surgery.

Data selection of P_ETCO₂ and rSO₂

The individual data files of P_ETCO₂ and rSO₂ were recorded continuously during the intervention period. The P_ETCO₂ and rSO₂ values were updated every 10 s and 5 s, respectively. For pharmacodynamic analysis, these data points were selected every 30 s.

Population pharmacodynamic analysis

We observed a slight time delay between the maximum P_ETCO₂ value and maximum rSO₂ value (1.8 ±1.5 min). NONMEM VII level 3 (ICON Development Solutions, Ellicott City, MD, USA) was used to fit a turnover model to the data.

$$\frac{d\left({\mathit{rSO}}_2\right)}{\mathit{dt}}=k_{\mathit{\text{in}}}\cdot H\left(c\right)-k_{\mathit{\text{out}}}\cdot {\mathit{rSO}}_2$$ (1)

$${\mathit{rSO}}_{2\_\mathit{\text{base}}}=\frac{k_{\mathit{\text{in}}}}{k_{\mathit{\text{out}}}}$$ (2)

where k_in is a turnover rate constant, k_out is a fractional turnover rate constant, and rSO_{2_base} is the baseline rSO₂. H(c) is a stimulation function to explain the relationship between P_ETCO₂ and rSO₂. Within the P_ETCO₂ range used in this study, the relationship is known to be linear 7. H(c) can be expressed as follows 9:

$$H\left(c\right)=1+\mathit{\text{slope}}\times P_{\mathit{ET}}{\mathit{CO}}_2$$ (3)

where slope is a slope factor in the stimulatory effect of P_ETCO₂ on the production of the response (rSO₂). To normalize the response of rSO₂ to P_ETCO₂ and to reduce the number of parameters to be estimated, rSO₂ data were normalized to individual baseline rSO₂ values. Hence, rSO_{2_base} was set to 1.

Interindividual random variabilities in pharmacodynamic parameters were estimated assuming a log‐normal distribution. Diagonal matrices were applied to estimate the various distributions of η, where η represented the interindividual random variability with a mean of zero and a variance of ω ². An additive residual error model was applied to the model building. NONMEM computed the minimum objective function value (OFV), a statistical equivalent to the –2 log likelihood of the model. An α level of 0.05, which corresponds to a reduction in the OFV of 3.84 (chi‐square distribution, degree of freedom = 1, P < 0.05), was used to distinguish between the hierarchical models 10. The covariates analysed were the time‐invariant age; height; weight; sex (1: male; 0: female); maximal percent decrease in luminal diameter of the ipsilateral or contralateral internal carotid artery; history of hypertension (HTN) or diabetes mellitus (DM; 1: presence; 0: absence); ejection fraction; E/A ratio; forced vital capacity (FVC); volume that has been exhaled at the end of the first second of forced expiration (FEV1); and FEV1/FVC ratio along with time‐varying SBP, mean blood pressure (MBP), and categorical data conversion of SBP (1: <90 mmHg; 2: ≥90 mmHg) and MBP (1: <60 mmHg, 2: ≥60 mmHg) during the intervention period. Nonparametric bootstrap analysis helped validate the models internally (fit4NM 3.3.3, Eun‐Kyung Lee and Gyu‐Jeong Noh; http://cran.r‐project.org/web/packages/fit4NM/index.html; last accessed: March 16, 2011) 11. Predictive checks were also performed using fit4NM 3.3.3 11. Deterministic simulations were performed to characterize the effect of covariates on rSO₂ by using the estimated pharmacodynamic parameters of the final model.

Statistics

Statistical analyses were conducted using R (version 3.3.2; R Foundation for Statistical Computing, Vienna, Austria) or SigmaStat version 3.5 for Windows (Systat Software, Inc, Chicago, IL, USA). Data are expressed as the mean ± standard deviation for normally distributed continuous variables, the median (25–75%) for non‐normally distributed continuous variables, or counts and percentages for categorical variables.

Results

Of the 32 patients enrolled, two were excluded from the analysis because of a technical error in data file storage. The characteristics of the remaining 30 patients are summarized in Table 1. In total, 1651 rSO₂ data points were used to determine the pharmacodynamic characteristics. Time courses of the P_ETCO₂, rSO₂, fractional rSO₂calculated by dividing rSO₂ by individual baseline rSO₂ values, and SBP during the intervention period are shown in Figure 1. SBPs during the intervention period ranged between 68 and 178 mmHg. Actual and fractional values of rSO₂ vs.P_ETCO₂ are displayed in Figure 2. As P_ETCO₂ increased, the rSO₂ value tended to increase.

Table 1.

Patient characteristics (n = 30)

Age, years	68.8 ± 8.0
Male/female	27/3
Weight, kg	62.8 ± 7.8
Height, cm	162.9 ± 7.0
ASA PS 2/3	21/9
Coexisting disease
Diabetes mellitus	12
Hypertension	21
Coronary artery disease	7
Maximal percent decrease in luminal diameter
Ipsilateral internal carotid artery, %	79.6 ± 7.2
Contralateral internal carotid artery, %	41.5 ± 20.9
Cardiac function by measured two‐dimensional echocardiography
Ejection fraction, %	62.5 (59–64)
E/A ratio	0.8 ± 0.2
Pulmonary function tests
FVC, l	3.4 ± 0.6
FEV1, l	2.4 ± 0.6
FEV1/FVC ratio	7.5 (6.4–8.0)
Concomitant medication
Antidiabetic drugs	11/30
Antihypertensive drugs	21/30
Lipid‐lowering drugs	24/30
Anticoagulation drugs	17/30
Aspirin	16/30
Others*	17/30

The data are expressed as mean ±standard deviation, median (25–75%) or count, as appropriate. ASA PS, American Society of Anesthesiologists Physical Status;E/A ratio, the ratio of peak velocity flow in early diastole (the E wave) to peak velocity flow in late diastole caused by atrial contraction (the A wave); FVC,forced vital capacity; FEV1, volume that has been exhaled at the end of the first second of forced expiration. Antidiabetic drugs: metformine (9), glimepiride (3), vildagliptin (2), gliclazide (1); antihypertensive drugs: amlodipine (7), atenolol (4), hydrochlorothiazide (4), losartan (3), carvedilol (3), valsartan (2), nebivolo (2), spironolactone (1), barnidipine (1), nisoldipine (1); lipid‐lowering drugs: atorvastatin (13), rosuvastatin (9), simvastatin (2); Anticoagulation drugs: clopidogrel (14), warfarin (1), rivaroxaban (1); * rebamipide (mucosal protection, 4), isosorbide mononitrate (treatment of angina pectoris, 3), choline alfoscerate (treatment of Alzheimer's disease and other dementias, 3), tamsulosin (treatment of symptomatic benign prostatic hyperplasia, 2), allopurinol (decrease of uric acid level, 2), celecoxib (nonsteroidal anti‐inflammatory drug, 2), ranitidine (decrease of stomach acid production, 1), cilostazol (alleviation of the symptoms of intermittent claudication, 1).

Figure 1.

Time courses of end‐tidal carbon dioxide (P_ETCO₂; A), regional cerebral oxygen saturation (rSO₂; B), fractional rSO₂ (C) and systolic blood pressure (D) during an intervention period to change P_ETCO₂ in patients undergoing carotid endarterectomy (n = 30). P_ETCO₂ is the partial pressure of CO₂ at the end of an exhaled breath. The intervention was conducted between skin incision and clamping of the carotid artery. The time at which the tidal volume and ventilation rate were decreased to raise P_ETCO₂ to 45 mmHg was defined as the reference time. The intervention period was set as the time elapsed between the reference time and the time when P_ETCO₂ reached 25 mmHg. Fractional rSO₂ was calculated by dividing rSO₂ by the individual baseline rSO₂ values. The baseline rSO₂ value was defined as the rSO₂ value at the reference time

Figure 2.

Regional cerebral oxygen saturation (rSO_2, A) and fractional rSO₂ (B) vs. end‐tidal carbon dioxide (P_ETCO₂) in patients undergoing carotid endarterectomy (n = 30). P_ETCO₂ is the partial pressure of CO₂ at the end of an exhaled breath. The intervention was conducted between skin incision and clamping of the carotid artery. The time at which the tidal volume and ventilation rate were decreased to raise P_ETCO₂ to 45 mmHg was defined as the reference time. The intervention period was set as the time elapsed between the reference time and the time when P_ETCO₂ reached 25 mmHg. Fractional rSO₂ was calculated by dividing rSO₂ by the individual baseline rSO₂ values. The baseline rSO₂ value was defined as the rSO₂ value at the reference time

The turnover model well described the time course of rSO₂. A history of HTN (1: presence; 0: absence) was a significant covariate for the slope, and it resulted in a greater improvement in the OFV (4.70, P < 0.05, degree of freedom = 1) than did the basic model (number of model parameters = 5). Categorical data conversion of SBP (1: <90 mmHg; 2: ≥90 mmHg) was a significant covariate for the k_out, and it resulted in a greater improvement in the OFV (88.43, P < 0.001, degree of freedom = 2) than did the OFV of a pharmacodynamic model that included HTN as a covariate for the slope only (number of model parameters = 6). Population pharmacodynamic parameter estimates, interindividual variability and median parameter values (2.5–97.5%) of the nonparametric bootstrap replicates of the final pharmacodynamic model of fractional rSO₂ are represented in Table 2. Predictive checks of the final pharmacodynamic model are presented in Figure 3. In total, 5.4% of the data were distributed outside of the 90% prediction intervals of the predictive check. The simulated response of fractional rSO₂ to P_ETCO₂ in a hypothetical patient is depicted in Figure 4.

Table 2.

Population pharmacodynamic parameter estimates, inter‐individual variability, and median parameter values (2.5–97.5%) of the nonparametric bootstrap replicates of the final pharmacodynamic model of fractional regional cerebral oxygen saturation (rSO₂)

Parameter	Estimate (RSE, %)	CV (%)	Median (2.5–97.5%)
kout (min−1)
SBP < 90 mmHg	3.59 (47.6)	215.2	4.42 (1.63–13.3)
SBP ≥ 90 mmHg	0.491 (24.8)	130.0	0.498 (0.360–0.675)
rSO2_base	1 (–)	–	–
Slope = θ1×HTN + (1 – HTN)×θ2
θ1	0.00321 (22.7)	87.2	0.00327 (0.00237–0.00439)
θ2	0.00664 (20.0)		0.00692 (0.00501–0.00946)
σ	0.00218 (15.7)	–	0.00223 (0.00179–0.00269)

A log‐normal distribution of interindividual random variability was assumed. Residual random variability was modelled using an additive error model. Nonparametric bootstrap analysis was repeated 2000 times. CV, coefficient of variation; k_out, fractional turnover rate constant; RSE, relative standard error = SE/mean×100 (%); SBP, categorical data conversion of systolic blood pressure during the intervention period, and every SBP was assigned a value of 1 (<90 mmHg) or 2 (≥90 mmHg). SBPs during the intervention period ranged between 68 mmHg and 178 mmHg. The intervention was conducted between skin incision and clamping of the carotid artery. The time at which the tidal volume and ventilation rate were decreased to raise end‐tidal carbon dioxide (P_ETCO₂) to 45 mmHg was defined as the reference time. The intervention period was set as the time elapsed between the reference time and the time when P_ETCO₂ reached 25 mmHg. rSO_{2_base}: baseline rSO₂, rSO_{2_base} was set to 1 because rSO₂ data were normalized to the individual baseline rSO₂values. Baseline rSO₂ value was defined as the rSO₂ value at the reference time. Slope: slope factor in the stimulatory effect of P_ETCO₂ on the production of the response (fractional rSO₂). HTN,hypertension;HTN was assigned a value of 1 (a person diagnosed with HTN) or 0 (a person without HTN).

Figure 3.

Predictive checks of the final pharmacodynamic model. A black+ indicates the observed fractional regional cerebral oxygen saturation (rSO₂). The solid red line and shaded areas indicate the 50% prediction line and 90% prediction intervals, respectively. Fractional rSO₂ was calculated by dividing rSO₂ by the individual baseline rSO₂ values. Baseline rSO₂ value was defined as the rSO₂ value at the reference time. The time at which the tidal volume and ventilation rate were decreased to raise end‐tidal CO₂ to 45 mmHg was defined as the reference time

Figure 4.

The simulated response of fractional regional cerebral oxygen saturation (rSO₂) to end‐tidal carbon dioxide (P_ETCO₂) in a hypothetical patient. Based on the presence of hypertension and whether the systolic blood pressure (SBP) was above or below 90 mmHg, four different cases were simulated. P_ETCO₂ and fractional rSO₂ data from a patient (ID 12) were used for the simulation analysis. SBPs observed during the intervention period ranged between 68 mmHg and 178 mmHg. The intervention was conducted between skin incision and clamping of the carotid artery. The time at which the tidal volume and ventilation rate were decreased to raise P_ETCO₂ to 45 mmHg was defined as the reference time. The intervention period was set as the time elapsed between the reference time and the time when P_ETCO₂ reached 25 mmHg. Fractional rSO₂ was calculated by dividing rSO₂ by the individual baseline rSO₂ values. The baseline rSO₂ value was defined as the rSO₂ value at the reference time

Discussion

CEA is a prophylactic treatment to reduce the incidence of stroke in patients who are at risk of stroke from emboli arising from atheromatous plaque in the carotid artery 12. Timely CEA can substantially reduce the risk of stroke, but the possibility of complications during the perioperative period should be also considered. Cerebrovascular accident and myocardial infarction are the two most severe perioperative complications 12. Especially during surgery, neurological derangement induced by impaired cerebral blood flow usually occurs during cross‐clamping of the carotid artery 2. The primary intervention in this event is the insertion of a shunt. It is also appropriate to maintain blood pressure perhaps 20% above the preoperative level to maintain the perfusion pressure across the Circle of Willis 12. A number of techniques and monitors, such as stump pressure, electroencephalogram, near‐infrared spectroscopy and transcranial Doppler, are available to monitor the occurrence of neurological derangement. Near‐infrared spectroscopy‐based rSO₂ is currently the most used in clinical practice due to its noninvasiveness and ease of use. During cross‐clamping of the carotid artery, a 5–6% increase in rSO₂ was observed at P_ETCO₂ 40–45 mmHg compared with P_ETCO₂ 30–35 mmHg in unshunted patients 6, which means that the rSO₂ value is changed by the change of P_ETCO₂. The turnover model presented in this study well explained the relationship between P_ETCO₂ and rSO₂ in patients with arteriosclerosis.

In the final pharmacodynamic model, a history of HTN was a significant covariate for the slope factor in the stimulatory effect of P_ETCO₂ on rSO₂. The response of rSO₂ to P_ETCO₂ increase was slow in patients with HTN than in those without HTN (see Figure 3). This can be explained by the fact that cerebrovascular carbon dioxide reactivity was more impaired in patients with HTN than in normotensive patients 13, 14. HTN induces changes in cerebrovascular structure and function, such as an increase in the wall/lumen ratio of the vessels and a decrease in the vasoconstrictory and vasodilatory abilities of the cerebral arterioles 14, 15. Cerebral remodelling caused by HTN is thought to be related to the slow response to P_ETCO₂ change.

In the operating room, a SBP of <80 mmHg is generally considered to indicate hypotension, and efforts are made to correct it 16. Autoregulation of cerebral blood flow refers to the intrinsic ability to maintain a constant perfusion in the face of blood pressure changes 17. In normal volunteers, the lower limit of autoregulation may be a MBP of 50–55 mmHg 18. However, in chronic HTN, the limits of autoregulation are shifted toward high blood pressure 17. Dynamic cerebral autoregulation is impaired in carotid artery stenosis 19. Taken together, cerebral blood flow may be reduced if SBP is <90 mmHg. Once cerebral blood flow is reduced, the compensatory mechanism to restore it will be activated. The increase in cerebral blood flow caused by the increase in P_ETCO₂ will also become large. This hypothesis may be supported by the results of a previous study showing that full restoration of cerebral blood flow to the baseline value was faster in hypocapnia after the step decrease in SBP, while the response was slower in normocapnia and hypercapnia 20. The results of the final pharmacodynamic model showed that the values of k_out were quite different when SBP was set at a cut‐off value of 90 mmHg (see Table 2). This difference led to a difference in the reaction of rSO₂ to P_ETCO₂ (refer to Figure 3). When a pharmacodynamic model was fitted to the data after a SBP of 90 mmHg or more was divided into two sections based on 140 mmHg, the k_out values were similar (90 ≤ SBP < 140 mmHg: k_out = 0.423; 140 ≤ SBP: k_out = 0.419). Although categorical data conversion of MBP (1: <60 mmHg; 2: ≥60 mmHg) was a significant covariate for k_out, the improvement of OFV (79.04) was less than that of SBP (88.43) as a covariate. The control stream of the final pharmacodynamic model that included a history of HTN and categorical data conversion of SBP are presented in the Appendix.

The difference in the reaction of rSO₂ to P_ETCO₂ was the largest in a hypothetical patient without HTN whose SBP remained below 90 mmHg (patient A) than in a patient with HTN whose SBP was maintained above 90 mmHg (patient B). Raising P_ETCO₂ from 25 to 45 mmHg showed a difference of 16% fractional rSO₂ between patients A and B (1.16–1.06 = 0.16; see Figure 3). Because the actual mean value of rSO₂ at the reference time was 55.8, this difference represented a difference of 8.9 in actual rSO₂ value.

In an earlier study, cerebrovascular carbon dioxide reactivity was greatly reduced in patients with severe cerebral vascular disease 21. The slope factor in the stimulatory effect of EtCO₂ on rSO₂ was about 2–3 times smaller in patients undergoing carotid endarterectomy than in patients from previous studies without cerebrovascular disease 7. In a previous study, DM was a significant covariate on the slope factor, but not in this study. Although DM was a significant covariate in the previous study, the slope factor was similar regardless of DM (presence of DM: slope factor = 0.011; absence of DM: slope factor = 0.015) 7. However, the slope factor of patients without HTN was about twice as large as that of patients with HTN in this study, which may suggest that HTN is a more significant covariate than is DM.

Cardiovascular lability is often observed in hypertensive patients undergoing general anaesthesia. These patients are prone to episodes of hypotension and HTN during surgery 22, 23. These adverse events are especially marked in patients undergoing CEA 12. An earlier study showed that HTN was seen in 25–58% of patients after CEA and hypotension was seen in 8–10% of patients 24. This study found that patients with HTN had lower cerebrovascular carbon dioxide reactivity than patients without HTN, which means that the ability to maintain cerebral blood flow is weakened. The decrease in SBP of these patients to <90 mmHg may lead to a decrease in cerebral blood flow. Hence, it is advisable to maintain SBP >90 mmHg in patients with HTN during CEA.

There are several limitations of the model. First, HTN is not well controlled and systolic blood pressure may be excessively high in patients with severe atherosclerosis. Because the model was constructed using limited blood pressure range data, it may not be possible to apply the results when the systolic blood pressure range is exceeded. Second, permissive hypercapnia can be helpful in mechanical ventilation strategies in patients with obstructive pulmonary disease 25. Changes in P_ETCO₂ during surgery may cause harm to patients with obstructive lung disease, so these patients were excluded from the clinical study. This model does not explain cerebrovascular carbon dioxide reactivity in patients with obstructive pulmonary disease. Third, it is not possible to predict change of rSO₂ and occurrence of neurological derangement during cross‐clamping of the carotid artery because the model was constructed using data before cross‐clamping.

There are also several issues to be considered as limitations of this study. First, cerebral near‐infrared spectroscopy measures the relative concentrations of oxyhaemoglobin and deoxyhaemoglobin, not cerebral blood flow. When evaluating cerebrovascular carbon dioxide reactivity, cerebral blood flow is commonly measured using transcranial Doppler 14, 18, 26. However, it is not widely used in clinical situations because of the small or absent transtemporal windows in some patients and the difficulty in keeping the probe steady 27. Therefore, rSO₂ is widely used because of its convenience and its validation as a measurement tool to detect cerebral ischaemia during carotid endarterectomy 4. As previously mentioned, the aim of this study was to quantitatively evaluate the effect of P_ETCO₂ on rSO₂, and not evaluating cerebrovascular carbon dioxide reactivity. We used the concept of cerebral carbon dioxide reactivity when interpreting the results of the pharmacodynamic analysis. The findings of this study are physiologically accountable and consistent with those of previous studies 14, 20, 21. Second, other factors affecting the dependent variable may not have been considered. Haemoglobin, total bilirubin, and inspired oxygen fraction are known as factors affecting rSO₂ measurement values 6, 28, 29. This study was conducted between skin incision and cross clamping of the carotid artery, and bleeding loss was negligible during this period. Therefore, haemoglobin levels would not have changed much during the intervention period. Total bilirubin levels were in the normal range in all patients, and the inspired oxygen fraction was kept constant. If both P_ETCO₂ and FiO₂ are involved in intervention, it may be difficult to evaluate the sole effect of EtCO₂ on rSO₂. Because the aim of this study was to evaluate the effect of P_ETCO₂ on rSO₂quantitatively, FiO₂ was fixed at a constant value and P_ETCO₂ was changed. In an earlier study that quantitatively analysed the effect of P_ETCO₂ on rSO₂ under general anaesthesia, FiO₂ was also fixed to a constant value 7.

In conclusion, the turnover model well described the change in rSO₂ according to the change in P_ETCO₂. HTN and SBP were significant covariates on the slope factor in the stimulatory effect of EtCO₂and fractional turnover rate constant, respectively. The presence of HTN attenuates the response of rSO₂ after a change in P_ETCO₂. When cerebral blood flow is in a state of decline caused by the decrease in SBP to <90 mmHg, the response of rSO₂ to P_ETCO₂ is increased. In anaesthetic management of patients undergoing carotid endarterectomy under general anaesthesia, it is advisable to maintain systolic blood pressure >90 mmHg in patients with HTN.

Competing Interests

All authors have completed the Unified Competing Interest form. No author has had any financial relationships over the previous 3 years with any organizations that might have an interest in this submitted work, and no author has any other relationships or has engaged in any activities that could appear to have influenced the submitted work.

This work was supported by the Korea Healthcare Technology R&D Project, Ministry of Health, Welfare and Family Affairs, Republic of Korea (Grant number: A102065–34).

Example of the control stream used in pharmacodynamic modelling

Turnover model

$PROB RUN# 45153 (turnover model)

$INPUT ID OID TIME CP DV MDV SEX AGE WT HT DM HTN MAXSTENO SBP MBP OPSBP

$DATA ETCO2_rSO2_join_covariates_BP_OID_fractional_DV_OPSBP2.csv IGNORE=@

; TIME: min

; CP: end-tidal CO2 (mmHg)

; DV: fractional rSO2

; SEX: M=1, F=0

; AGE: yr, WT: kg, HT: cm

; DM: 1=Yes, 0=No

; HTN: 1=Yes, 0=No

; MAXSTENO: maximal carotid artery stenosis

; BP: blood pressure (S: systol, M: mean, D: diastol)

; OPSBP: 1: SBP<90, 2: 90<=SBP

; OPMBP: 1: MBP<60, 2: 60<=MBP

$SUBROUTINE ADVAN=6 TOL=3

$MODEL COMP (EFF)

$PK

TH1 = THETA(1)

TH2 = THETA(2)

TH3 = THETA(3)

TH4 = THETA(4)

TH5 = THETA(5)

IF (OPSBP.EQ.1) KOUT=TH1*EXP(ETA(1))

IF (OPSBP.EQ.2) KOUT=TH2*EXP(ETA(2))

BRSO = TH3*EXP(ETA(3))

SLOPE = (TH4*HTN + (1-HTN)*TH5)*EXP(ETA(4))

KIN = KOUT*BRSO

IF(A_0FLG.EQ.1) A_0(1)=BRSO

$DES

FCO2=1 + SLOPE*CP

DADT(1) = KIN*FCO2 - KOUT*A(1)

$ERROR

ERSO2 = A(1)

IPRED = ERSO2

W = 1

IRES = DV - IPRED

IWRES = IRES / W

Y = IPRED + W*EPS(1)

$THETA ;#4

(0, 2) ; KOUT_SBP<90

(0, 0.5) ; KOUT_90<=SBP

1 FIX ; BRSO

(0, 0.1, 1) ; SLOPE_HTN

(0, 0.1, 1) ; SLOPE_No_HTN

$OMEGA ;#3

0.4 ; IIV_KOUT_SBP<90

0.4 ; IIV_KOUT_90 <=SBP

0 FIX ; IIV_BRSO

0.2 ; IIV_SLOPE

$SIGMA ;#1

0.1 ; EPS

$ESTIMATION NOTBT NOOBT NOSBT SIGL=3 NSIG=1 MAXEVAL=9999 PRINT=5 METHOD=1 INTER MSFO=45153.MSF NOABORT

$COVARIANCE PRINT=E

Ki, S.‐H. , Rhim, J.‐H. , Park, J.‐H. , Han, Y.‐J. , Cho, Y.‐P. , Kwon, T.‐W. , Choi, B.‐M. , and Noh, G.‐J. (2018) Quantitative analysis of the effect of end‐tidal carbon dioxide on regional cerebral oxygen saturation in patients undergoing carotid endarterectomy under general anaesthesia. Br J Clin Pharmacol, 84: 292–300. doi: 10.1111/bcp.13441.